What mechanical work must you do to lift a uniform log that is 3.3m long and has a mass of 100kg from the horizontal to a vertical position? [Hint: Use the work-energy principle.]

Well, to lift that long log, you'll need some serious leg muscles! But let's calculate the mechanical work using the work-energy principle.

First, we need to find the gravitational potential energy of the log when it's in a vertical position. The gravitational potential energy is given by the formula: PE = mgh, where m is the mass, g is the acceleration due to gravity, and h is the height.

Now, in the horizontal position, the height is zero, and when you lift it vertically, the height becomes 3.3m. So, the change in height, h, is 3.3m.

The acceleration due to gravity, g, is approximately 9.8 m/s².

Plug in the values: PE = (100kg) * (9.8 m/s²) * (3.3m).

Now, remember that work done equals the change in potential energy. So, the work done to lift the log is: W = PE = (100kg) * (9.8 m/s²) * (3.3m) = 32340 J.

So, to answer your question, you need to do approximately 32,340 Joules of work to lift that log. Or you can just get a strong friend to do it for you and save your energy for less log-lifting endeavors!

To lift the log from a horizontal to a vertical position, you need to perform mechanical work against gravity. The work done is equal to the change in potential energy of the log.

The potential energy due to gravity is given by the formula:

PE = mgh

Where:
PE is the potential energy
m is the mass of the log
g is the acceleration due to gravity (approximately 9.8 m/s²)
h is the height of the log

In this case, the height is the vertical distance you lift the log, which is 3.3 meters.

Using the given values, the mechanical work required is:

PE = (100 kg) * (9.8 m/s²) * (3.3 m)
= 32340 Joules

Therefore, the mechanical work required to lift the log is 32340 Joules.

To find the mechanical work required to lift the log, we can use the work-energy principle, which states that the work done on an object is equal to the change in its kinetic energy. In this case, since the log starts from rest and only experiences a change in potential energy, we can consider the work done to be equal to the change in potential energy.

The potential energy of an object in a gravitational field is given by the equation:

Potential Energy = mgh

where m is the mass of the object, g is the acceleration due to gravity, and h is the height change.

In this scenario, the log is lifted from the horizontal to the vertical position, implying a change in height of h = 3.3 m. The mass of the log is given as 100 kg, and the acceleration due to gravity is approximately 9.8 m/s^2.

Therefore, the mechanical work required to lift the log can be calculated as:

Work = Potential Energy = mgh
= (100 kg) * (9.8 m/s^2) * (3.3 m)
≈ 32340 Joules

Hence, the required mechanical work to lift the log is approximately 32340 Joules.

the work done is by lifting it up

so you can use mgh
The tricky part here is that you need to consider where the center of gravity is and it would be the center of the log so the COG is lifted half of the total length of the log

100kg x 9.8 N/Kg x 1.65 meters